Find a equation for a sinusoidal function that has period 2 pie amplitude 1 and contains the point 3 pie over 2, 0

Thus, the equation of sinusoidal function is

Explanation:

The standard form of sine function is:

where,

a = amplitude

2π/b = period

h = phase shift

k = vertical displacement

Step wise formation of the equation:

In sine curve, the basic model is:

y = sinx

Apply a vertical stretch/shrink to get the desired amplitude:

new equation:    

y  =  a sin x

y = 1 sinx

For  k > 0, the curve y = sin kx has period 2π/ k

The period is 2. So the value of k is

2π = 2π / b

b = 1

So, the equation becomes:

y = 1 sin x

Phase shift is 3π/2. The new equation is

Vertical displacement, k = 0

So, the equation is

Thus, the equation of sinusoidal function is

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: